Multi wave, kink, breather, interaction solutions and modulation instability to a conformable third order nonlinear Schrödinger equation

The purpose of this work is the examine the three-waves, double exponential, homoclinic breather, and periodic cross kink-soliton solutions for a third-order fractional nonlinear Schrödinger equation (3-FNLS). This model which is vital in fiber optics, explains the propagation of light in optical fibers when ultra-short pulses are produced. We define the model in terms of the conformable time fractional derivative operator so that the model could give a better description of the physical aspect. By picking the activation function in Hirota bilinear form, as the hyperbolic, trigonometric and exponential function along with suitable dispose of parameters, we acquire the three-waves, double exponential, homoclinic breather, and periodic cross kink-soliton auspiciously. Additionally, we have elucidated some three-dimensional and contour portraits to foresee the wave dynamics. These acquired new solutions that do not exist in the literature include some free constants and thereby can be significant to describe variety in qualitative aspects of wave phenomena. At last, we also check the stability of the governing model. By executing the modulation instability analysis, we scrutinize the stability analysis of the yielded exact solutions and the movement role of the waves.